Revealing the pulse-induced electroplasticity by decoupling electron wind force

Micro/nano electromechanical systems and nanodevices often suffer from degradation under electrical pulse. However, the origin of pulse-induced degradation remains an open question. Herein, we investigate the defect dynamics in Au nanocrystals under pulse conditions. By decoupling the electron wind force via a properly-designed in situ TEM electropulsing experiment, we reveal a non-directional migration of Σ3{112} incoherent twin boundary upon electropulsing, in contrast to the expected directional migration under electron wind force. Quantitative analyses demonstrate that such exceptional incoherent twin boundary migration is governed by the electron-dislocation interaction that enhances the atom vibration at dislocation cores, rather than driven by the electron wind force in classic model. Our observations provide valuable insights into the origin of electroplasticity in metallic materials at the atomic level, which are of scientific and technological significances to understanding the electromigration and resultant electrical damage/failure in micro/nano-electronic devices.


Evaluation of thermal effects
Under electrical current, the unavoidable Joule heat may soften materials by reducing the lattice resistance and activating the dislocation motion 1 . In classic theory, the Joule heat, associated thermal stress and thermal gradient serve as the major thermal effects for electroplasticity 1,2 . In our experiments, however, the thermal effects of nanosecond electrical pulse should be negligible, as discussed below.

Estimation of the temperature rise during the nanosecond pulse
The temperature rise induced by the electrical pulse in bulk sample can be given by 3 : where is the voltage, is the pulse width, is the resistance, is the specific heat capacity and m is the mass of specimen. Due to the limitation of experimental setup, it is difficult to accurately measure the exact resistance of Au nanocrystal, and may also deviate from the value of bulk samples 4 . Besides, with the ultrahigh thermal diffusivity (1.27 × 10 -4 m 2 s -1 ) and thermal conductivity (317.422 W m -1 K -1 ) of Au matrix, the actual temperature rise in the specimen could be less than the calculated value 3 . Here, we managed to conduct an in situ experiment to estimate . Firstly, we use Au nanocrystals with the same size and morphology as the specimen in Fig. 2 If we can obtain the critical pulse voltage ( ) that can melt the Au nanocrystal (the 8 melt point of bulk Au is 1064 °C), the temperature rise under the pulse of (1.0 V, 3 ns) can be roughly estimated by: Following this idea, we conducted several controlled electropulsing experiments to melt the Au nanocrystals. Supplementary Fig. 6 shows an example. The melt voltage ( ) of the pulse was measured to be 5 ~ 6 V. With the equation (3), we can roughly obtain a temperature rise in the range of 29 °C ~ 42 °C for the pulse of (1.0 V, 3 ns) and 83 °C ~ 120 °C for the pulse of (1.7 V, 3 ns). Such temperature rises, in conjunction with the nanosecond pulse width, are too small to activate the dislocation motion, compared with the temperature rise of several hundred degrees with long-time exposure reported in other works 5,6 . Thus, the driving force of dislocation motion should mainly come from the direct electron-dislocation interaction.

Estimation of the thermal dissipation of pulse current
The dissipation time of thermal heating is further estimated to evaluate its contribution to the ITB migration. Theoretically, the distance of thermal diffusion over time (diffusion length ) can be calculated by 1,7 : where is the thermal diffusivity of specimen and is the time of thermal diffusion. In this equation, can be determined by: where is the thermal conductivity,  is the density and is the specific heat capacity.
At room temperature, the typical values of these parameters for Au are 8

Discussion on the pre-exponential factor ̇0
Generally, the plastic flow of materials is thermally-activated and the drift electrons can influence the pre-exponential factor ̇0 9 : where , is the mobile dislocation density, is the Burgers vector, is the area of This enhanced vibration can be viewed as an additional lattice vibration activated beyond the normal vibration of lattice, since it is a localized phenomenon near the dislocation core, activated by the electron-dislocation interaction. 12

Quantification of the stress state
Supplementary Fig. 8 schematically illustrated the three typical migration situations (corresponding to the three stages in Fig. 3), which are discussed as follows.

Stage Ⅰ: x = x 1 , non-directional migration
When the ITB was far away from the free surface, 1 was relatively small. In It needs to note that between pulses, relaxation-induced ITB migrations occurred and all proceeded toward the free surface. This implies that the residual stress induced by electropulsing, as a driving force, was too small to work against − and 1 . Thus, the partials can only slip toward free surface (driven by the 1 and residual stress) without the help of electrical pulses.

Stage Ⅱ: x = x 2 , directional migration
When the ITB approached one side of the sample surface (e.g., at Point l in Fig.   3a, the distance between ITB and left free surface was 9.9 nm and 22.2 nm for right free surface), increased gradually to some value of 2 , while remained unchanged (the pulse parameters and sample geometry are the same). At this moment, − + 2 > . As a result, the ITB cannot migrate away from free surface, and a directional migration toward left surface was exhibited.

Stage Ⅲ: x = x 3 , surface annihilation
As the ITB migrated close to the free surface, increased to a level higher than − (denoted as 3 ). Under this condition, dislocations of ITB would move 13 continuously and annihilate to the free surface upon electropulsing, as shown by the final migration for 9.9 nm without any stop in Fig. 3j.
According to the analysis above, we can obtain that: Thus, by calculating the magnitudes of − , 1 and 2 , the value of can be roughly estimated, as discussed following. 14 Firstly, we need to calculate the magnitudes of 1 and 2 . Since the ITB was deviated from the sample center toward the left surface slightly, the distances between left and right free surface must be considered at the same time when calculating the image stress. And the total image stress is 12 :

Supplementary
The Substituting these values into the equation (8), the values of 1 and 2 are estimated to be 1.4 × 10 -2 GPa and 3.7 × 10 -2 GPa, respectively.
It is kind of hard to precisely calculate the magnitude of − , due to the complex stress field of ITB. But in our experiments, by analyzing the migration dynamics of ITB, the value of − can be estimated as follow: in stage Ⅰ and Ⅱ, − was larger than because partial dislocations of ITB eventually stopped to move after the electropulsing. But in stage Ⅲ, ITB migrated 9.9 nm and annihilated at free surface under the same pulse conditions in stage Ⅰ and Ⅱ. This unusual migration indicates that after a slight migration under pulse current, increased and became lager than − , resulting a spontaneous migration toward surface continuously. The analyses above imply that = 2 is a transition point where − ≈ 2 , corresponding to a − value of ~ 3.7 × 10 -2 GPa. Substituting the values of − , 1 and 2 in equation (7), is determined to be in the range of 5.1 × 10 -2 GPa -7.4 × 10 -2 GPa.

Measurements of electrical resistance and current density of Au nanocrystal
Resistances of Au nanocrystals were measured to quantify the current density under electropulsing. Considering the intrinsic experimental error in two-wire resistance sensing, the contrast experiment was carried out to measure the resistances of Au nanocrystals. A source meter instrument (Keithley 2611B SYSTEM Source Meter®) was used as a constant current output.
Firstly, the resistances of the circuit with an Au wire (0.25 mm in diameter) were measured several times under different conditions, including before the application of pulses, during the intervals of pulses and after the application of several pulses ( Supplementary Fig. 5a). The measured resistance 1 is: where 1 is the measured voltage of the external circuit, is the resistance of Au wire, and is the lead resistance and contact resistance, respectively. The room temperature bulk resistivity of Au is quoted to be 2.2 μΩ cm 15 and thus the calculated resistance ( ) of Au wire is 1.12 × 10 -3 Ω, which is negligible. So 1 ≈ 2 + 2 , which was measured to be 9.7 Ω ~ 10.1 Ω.
Then, the resistances of the circuit with Au nanocrystal were measured in the same way ( Supplementary Fig. 5b), where the resistances of lead and contact remained unchanged. The measured resistance 2 is: where, is the resistance of nanocrystal. As shown in Supplementary Fig. 5c (11) where is the pulse voltage (1.0 V) and is the radius of the cross section at the ITB (~ 16 nm). Given a total measured resistance of ~ 75 Ω, the current density is estimated to be ~ 1.7 × 10 9 A cm -2 . 17

Evaluation of the skin effect
The skin effect, referring to the localization or concentration of current near a specimen surface 16 , may influence the stress magnitude of electron-dislocation interaction near free surface.
To evaluating the skin effect in our experiments, we have measured the output of the pulse generator using an oscilloscope, as shown in Supplementary Fig. 9. When we applied a pulse of (1.0 V, 3 ns), the measured pulse was (0.93 V, 2.83 ns) as shown by point D and time duration between B and F in Supplementary Fig. 9, matching well with the parameters we set, though an acceptable error did exist.

Supplementary
where is the frequency of the pulse (which is 200MHz based on the period given below), µ is the permeability, is the resistivity of the specimen and is the period of the pulse. For one pulse applied in our experiment, T ≈ 5 ns (see Supplementary Fig.   9), µ = 4 × 10 -7 H m -1 , ≈ 20 μΩ cm (Supplementary Discussion 4). Substituting these values into equation (12), we obtain a skin depth δ of ~ 1.6 × 10 -5 m. This value is about three orders larger than the diameters of our specimens (typically less than 20 nm, on the order of 10 -8 m). Therefore, the current should be uniformly distributed throughout the specimens in our experiment, with less contribution of skin effect.

Evaluation of the resistive-capacitive effects
The resistive-capacitive (RC) effects resulted from the stray capacitance in the circuit might lengthen the pulse width, which could influence the thermal dissipation and skin effect. However, in our experiments, these effects arise from the longer pulse should be negligible. Even if the pulse width is extended to 10 ns due to the RC effects in practice, the diffusion length in thermal dissipation is calculated to be ~1130 nm (based on the equation (4) in Supplementary Discussion 1.2), which is much larger than the maximum length of Au nanocrystals (around 100 nm); while the skin depth is calculated to be ~2.3× 10 -5 m (based on the equation (12) of Supplementary Discussion 5), which is about three orders larger than the diameters of our specimens (typically less than 20 nm, on the order of 10 -8 m). Thus, the variation in the pulse width is insignificant on the conclusion of our experiments.